Problem: Rewrite as a simplified fraction. ${3.41\overline{4} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3414.4444...\\ 100x &= 341.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3073}$ ${x = \dfrac{3073}{900}} \text{or} {3 \dfrac{373}{900}}$